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If ABCDEF is a regular hexagon then vec(...

If ABCDEF is a regular hexagon then `vec(AD)+vec(EB)+vec(FC)` equals :

A

0

B

2AB

C

3AB

D

4AB

Text Solution

Verified by Experts

The correct Answer is:
D
A regular hexagon ABCDEF.

We know from the hexagon that AD is parallel to BC orr `AD=2BC` is parallel to FA or EB=2FA and FC is parallel to AB or FC=2AB.
Thus, `AD+EB+FC=2BC+2FA+2AB`
`=2(FA+AB+BC)=2(FC)=2(2AB)=4AB`.
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ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
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  2. If A,B and C are the vertices of a triangle with position vectors vec(...

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  4. Find the discriminant of the quadratic equation x^2+3x+2

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  5. In a regular hexagon ABCDEF, prove that AB+AC+AD+AE+AF=3AD.

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  6. Find the dot product of the vector 2hati+3hatj+1hatk and 1hati+2hatj+3...

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  7. If a and b are two non-zero and non-collinear vectors then a+b and a-b...

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  8. If |veca+ vecb| lt | veca- vecb|, then the angle between veca and vecb...

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  9. The magnitudes of mutually perpendicular forces a,b and c are 2,10 and...

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  10. If hati-3hatj+5hatk bisects the angle between hata and -hati+2hatj+2ha...

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  11. Find the discriminant of the quadratic equation x^2+5x+4=0 and also fi...

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  12. Given three vectors vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja ...

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  13. ' I ' is the incentre of triangle A B C whose corresponding sides are ...

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  14. If vecx and vecy are two non-collinear vectors and ABC is a triangle w...

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  15. If vec xa n d vec y are two non-collinear vectors and a, b, and c r...

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  16. If the resultant of two forces is equal in magnitude to one of the ...

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  17. If vec b is a vector whose initial point divides the join of 5 hat ...

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  18. find the term independent of x in the expansion of (2x-1/x)^2 ?

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  19. If veca and vecb are two unit vectors and theta is the angle between t...

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  20. A, B, C and D have position vectors veca, vecb, vecc and vecd, repecti...

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